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SUMMARY:Li Chen (Massachusetts Institute of Technology)
DTSTART:20201207T170000Z
DTEND:20201207T175000Z
DTSTAMP:20260423T010138Z
UID:anpdews/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/45/"
 >Effective equations of quantum mechanics and phase transitions</a>\nby Li
  Chen (Massachusetts Institute of Technology) as part of HA-GMT-PDE Semina
 r\n\n\nAbstract\nEffective equations of many-body quantum mechanics form t
 he backbone of many fields of modern physics. Notable examples of effectiv
 e equations include the Hartree-Fock\, Kohn-Sham\, and Bogoliubov-de Genne
 s (BdG) equations. Although their physical derivations vary\, we will revi
 ew an unified formal mathematical frame work for their derivations (if tim
 e permits). In this frame work\, the BdG equations are the most general fo
 rm of effective equations. Physically\, they form a microscopic descriptio
 n of superconductivity. When the temperature T is lower than a certain cri
 tical Tc\, superconducting solutions emerge. In this talk\, we will demons
 trate the the existence of solutions to the BdG equations via variational 
 arguments and show energy instability (hence the formation of a supercondu
 cting order parameter) when T < Tc. \n\nThis is a joint work with I. M. Si
 gal\n
LOCATION:https://researchseminars.org/talk/anpdews/45/
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